Related papers: Invariant types in NIP theories
This paper is a sequel to [1] and considers definability in differential-henselian monotone fields with c-map and angular component map. We prove an Equivalence Theorem among whose consequences are a relative quantifier reduction and an NIP…
We construct a degree-type otopy invariant for equivariant gradient local maps in the case of a real finite dimensional orthogonal representation of a compact Lie group. We prove that the invariant establishes a bijection between the set of…
We refine results of Gannon [G21, Theorem 4.7] and Simon [S15a, Lemma 2.8] on equivalences of convergent Morley sequences. We then introduce the notion of eventual $NIP$, as a property of a model, and give a variant of [KP18, Corollary…
We first rigourously establish, for any N, that the toroidal modular invariant partition functions for the (not necessarily unitary) W_N(p,q) minimal models biject onto a well-defined subset of those of the SU(N)xSU(N) Wess-Zumino-Witten…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
A theory of finite type invariants for arbitrary compact oriented 3-manifolds is proposed, and illustrated through many examples arising from both classical and quantum topology. The theory is seen to be highly non-trivial even for…
We build on our previous paper \cite{constructive} by using the general method introduced there in conjunction with invariant theory. This yields quantifier elimination results for the classical quaternions, octonions, as well as other…
We investigate the category of discrete topological spaces, with emphasis on inverse systems of height $\omega_1$. Their inverse limits belong to the class of $P$-spaces, which allows us to explore dimensional types of these spaces.
We will report some results concerning the Yamabe problem and the Nirenberg problem. Related topics will also be discussed. Such studies have led to new results on some conformally invariant fully nonlinear equations arising from geometry.…
We introduce a new topological invariant, which is a nonnegative integer, of compact manifolds with boundaries associated with a kind of decomposition of them. Let M and N be m-dimensional compact connected manifolds with boundaries. The…
We introduce the notion of weight system for finite type invariants of integral homology 3-spheres, and we show that invariants of type m are determined, modulo invariants of type m-1, by their associated weight system.
This paper addresses a theory of R(p,q)-deformed combinatorics in discrete probability. It mainly focuses on R(p,q)-deformed factorials, binomial coefficients, Vandermonde's formula, Cauchy's formula, binomial and negative binomial…
This paper introduces an expressive class of quotient-inductive types, called QW-types. We show that in dependent type theory with uniqueness of identity proofs, even the infinitary case of QW-types can be encoded using the combination of…
The directional differentiability of the solution map of obstacle type quasi-variational inequalities (QVIs) with respect to perturbations on the forcing term is studied. The classical result of Mignot is then extended to the…
In this paper, we define indexed type theories which are related to indexed ($\infty$-)categories in the same way as (homotopy) type theories are related to ($\infty$-)categories. We define several standard constructions for such theories…
We express continuous $\times p,\times q$-invariant measures on the unit circle via some simple forms. On one hand, a continuous $\times p,\times q$-invariant measure is the weak-$*$ limit of average of Dirac measures along an irrational…
We introduce the class of unshreddable theories, which contains the simple and NIP theories, and prove that such theories have exactly saturated models in singular cardinals, satisfying certain set-theoretic hypotheses. We also give…
In this paper, we give a very general criterion for elimination of imaginaries using an abstract independent relation. We also study germs of definable functions at certain well-behaved invariant types. Finally we apply these tools to the…
By studying periodic points for rational maps on $\bm{C}^d$ with $p$ invariants, we show that they form an invariant variety of dimension $p$ if the periodicity conditions are `fully correlated', and a set of isolated points if the…
We describe a non-extensional variant of Martin-L\"of type theory which we call two-dimensional type theory, and equip it with a sound and complete semantics valued in 2-categories.